Appendix
Domestic and Foreign Sources of Growth in National Income
International macroeconomic accounting dictates that an economy’s current account deficit, or its use of foreign saving through net capital inflow or foreign investment, equals its investment- saving gap (CAD = S* = I - S). Hence, increases in the domestic real capital stock are partly financed by domestic saving and partly by foreign saving (ΔK = I = S + S*).
Accordingly, a macroeconomic production function may be specified following Makin (2006) as
Y = f(A,Kd, K*, L) (1a)
where Kd is that part of the total domestic capital stock that has been funded by domestic saving and K* is that part of the total domestic capital stock has been foreign-financed.
By totally differentiating this open economy production function, the sources of increased gross domestic product in the short run are shown to be
(2a)
where fi denotes the derivative of Y for i - A,Kd, K*, L.
For economies that are net borrowers, national output and national disposable income diverge to the extent of net income paid abroad. Hence,
Yn = Y - r* K* (3a)
where Yn is national disposable income and r* is the effective servicing cost of foreign capital (inclusive of dividends) on external liabilities.
So,
(4a)
The effective interest rate paid to foreigners may vary from interval to interval as world interest rates fluctuate or as any risk premium varies through time.
From the above equations, the sources of national income growth can therefore be shown as
(5a)
The first bracketed term includes domestic sources of growth whereas the second bracketed term includes foreign sources. Hence, national income gains can be attributed to domestic sources, 
, and foreign sources, 
, such that
(6a)
Dividing through by national income,
| National Income Growth = | Domestic Contribution + | Foreign Contribution |
(%) |
(%) |
(%) |
To estimate the net contribution of foreign capital, it is necessary from (5a) to derive values in real terms for each of the variables in the expression
(7a)
